Answer:
-254 kJ
Explanation:
By Hess' Law, the enthalpy of a global reaction is the sum of the enthalpies of the steps reactions. If the reaction is multiplied by a constant, the enthalpy must be multiplied by the same value, and if the reaction is inverted, the signal of the enthalpy must be inverted too. Thus, the steps reactions and their enthalpies are:
CO₂(g) + 3H₂(g) → CH₃OH(l) + H₂O(l) ΔH = -131 kJ (multiply by 2)
2CH₃OH(l) → CH₃OCH₃(g) + H₂O(l) ΔH = 8 kJ
2CO₂(g) + 6H₂(g) → 2CH₃OH(l) + 2H₂O(l) ΔH = -262 kJ
2CH₃OH(l) → CH₃OCH₃(g) + H₂O(l) ΔH = 8 kJ
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2CO₂(g) + 6H₂(g) → CH₃OCH₃(g) + 3H₂O(l)
The bolded substances have the same amount on both sides, so they are canceled.
ΔH = -262 + 8
ΔH = -254 kJ
